Question: Solve for $x$ and $y$ using elimination. ${6x-2y = 10}$ ${5x+2y = 23}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {6x-2y = 10}\thinspace$ to find $y$ ${6}{(3)}{ - 2y = 10}$ $18-2y = 10$ $18{-18} - 2y = 10{-18}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {5x+2y = 23}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ + 2y = 23}$ ${y = 4}$